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Sum
Find the polar co-ordinates of points whose Cartesian co-ordinates are:
(–1, –1)
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Solution
Here, x = – 1 and y = – 1
∴ the point lies in the third quadrant.
Let the polar coordinates be (r, θ)
∴ r2 = x2 + y2 = ( – 1)2 + ( – 1)2 = 1 + 1 = 2
∴ r = `sqrt(2)` ...[∵ r > 0]
tanθ = `y/x = (-1)/(-1)` = 1
Since the point lies in the third quadrant and 0 ≤ θ < 2π,
tanθ = 1
= tan 45°
= tan (180° + 45°) ...[∵ tanθ is periodic function with period π = 180°]
∴ tanθ = tan225°
∴ θ = 225°
∴ the polar coordinates of the given point are `(sqrt(2), 225^circ)`.
Concept: Polar Co-ordinate System
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